src/HOL/Tools/datatype_abs_proofs.ML
author wenzelm
Tue Oct 25 18:18:49 2005 +0200 (2005-10-25)
changeset 17985 d5d576b72371
parent 17959 8db36a108213
child 18314 4595eb4627fa
permissions -rw-r--r--
avoid legacy goals;
berghofe@5177
     1
(*  Title:      HOL/Tools/datatype_abs_proofs.ML
berghofe@5177
     2
    ID:         $Id$
wenzelm@11539
     3
    Author:     Stefan Berghofer, TU Muenchen
berghofe@5177
     4
berghofe@5177
     5
Proofs and defintions independent of concrete representation
berghofe@5177
     6
of datatypes  (i.e. requiring only abstract properties such as
berghofe@5177
     7
injectivity / distinctness of constructors and induction)
berghofe@5177
     8
berghofe@5177
     9
 - case distinction (exhaustion) theorems
berghofe@5177
    10
 - characteristic equations for primrec combinators
berghofe@5177
    11
 - characteristic equations for case combinators
berghofe@5177
    12
 - equations for splitting "P (case ...)" expressions
berghofe@5177
    13
 - datatype size function
berghofe@5177
    14
 - "nchotomy" and "case_cong" theorems for TFL
berghofe@5177
    15
berghofe@5177
    16
*)
berghofe@5177
    17
berghofe@5177
    18
signature DATATYPE_ABS_PROOFS =
berghofe@5177
    19
sig
berghofe@13641
    20
  val prove_casedist_thms : string list ->
berghofe@13641
    21
    DatatypeAux.descr list -> (string * sort) list -> thm ->
berghofe@13641
    22
    theory attribute list -> theory -> theory * thm list
berghofe@13641
    23
  val prove_primrec_thms : bool -> string list ->
berghofe@13641
    24
    DatatypeAux.descr list -> (string * sort) list ->
berghofe@5177
    25
      DatatypeAux.datatype_info Symtab.table -> thm list list -> thm list list ->
berghofe@8477
    26
        simpset -> thm -> theory -> theory * (string list * thm list)
berghofe@13641
    27
  val prove_case_thms : bool -> string list ->
berghofe@13641
    28
    DatatypeAux.descr list -> (string * sort) list ->
wenzelm@8436
    29
      string list -> thm list -> theory -> theory * (thm list list * string list)
berghofe@13641
    30
  val prove_split_thms : string list ->
berghofe@13641
    31
    DatatypeAux.descr list -> (string * sort) list ->
berghofe@5177
    32
      thm list list -> thm list list -> thm list -> thm list list -> theory ->
berghofe@5177
    33
        theory * (thm * thm) list
berghofe@13641
    34
  val prove_size_thms : bool -> string list ->
berghofe@13641
    35
    DatatypeAux.descr list -> (string * sort) list ->
berghofe@5177
    36
      string list -> thm list -> theory -> theory * thm list
berghofe@13641
    37
  val prove_nchotomys : string list -> DatatypeAux.descr list ->
berghofe@13641
    38
    (string * sort) list -> thm list -> theory -> theory * thm list
berghofe@13641
    39
  val prove_weak_case_congs : string list -> DatatypeAux.descr list ->
berghofe@13641
    40
    (string * sort) list -> theory -> theory * thm list
berghofe@13641
    41
  val prove_case_congs : string list ->
berghofe@13641
    42
    DatatypeAux.descr list -> (string * sort) list ->
berghofe@5177
    43
      thm list -> thm list list -> theory -> theory * thm list
berghofe@5177
    44
end;
berghofe@5177
    45
wenzelm@8436
    46
structure DatatypeAbsProofs: DATATYPE_ABS_PROOFS =
berghofe@5177
    47
struct
berghofe@5177
    48
berghofe@5177
    49
open DatatypeAux;
berghofe@5177
    50
berghofe@5177
    51
(************************ case distinction theorems ***************************)
berghofe@5177
    52
wenzelm@8436
    53
fun prove_casedist_thms new_type_names descr sorts induct case_names_exhausts thy =
berghofe@5177
    54
  let
wenzelm@6427
    55
    val _ = message "Proving case distinction theorems ...";
berghofe@5177
    56
skalberg@15570
    57
    val descr' = List.concat descr;
berghofe@5177
    58
    val recTs = get_rec_types descr' sorts;
skalberg@15570
    59
    val newTs = Library.take (length (hd descr), recTs);
berghofe@5177
    60
berghofe@8477
    61
    val {maxidx, ...} = rep_thm induct;
wenzelm@8305
    62
    val induct_Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct)));
berghofe@5177
    63
berghofe@5177
    64
    fun prove_casedist_thm ((i, t), T) =
berghofe@5177
    65
      let
berghofe@5177
    66
        val dummyPs = map (fn (Var (_, Type (_, [T', T'']))) =>
berghofe@5177
    67
          Abs ("z", T', Const ("True", T''))) induct_Ps;
berghofe@8477
    68
        val P = Abs ("z", T, HOLogic.imp $ HOLogic.mk_eq (Var (("a", maxidx+1), T), Bound 0) $
berghofe@5177
    69
          Var (("P", 0), HOLogic.boolT))
skalberg@15570
    70
        val insts = Library.take (i, dummyPs) @ (P::(Library.drop (i + 1, dummyPs)));
wenzelm@17985
    71
        val cert = cterm_of thy;
berghofe@5177
    72
        val insts' = (map cert induct_Ps) ~~ (map cert insts);
skalberg@15570
    73
        val induct' = refl RS ((List.nth
skalberg@15570
    74
          (split_conj_thm (cterm_instantiate insts' induct), i)) RSN (2, rev_mp))
berghofe@5177
    75
wenzelm@17985
    76
      in
wenzelm@17985
    77
        standard (Goal.prove thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t)
wenzelm@17985
    78
          (fn prems => EVERY
wenzelm@17985
    79
            [rtac induct' 1,
wenzelm@17985
    80
             REPEAT (rtac TrueI 1),
wenzelm@17985
    81
             REPEAT ((rtac impI 1) THEN (eresolve_tac prems 1)),
wenzelm@17985
    82
             REPEAT (rtac TrueI 1)]))
berghofe@5177
    83
      end;
berghofe@5177
    84
berghofe@5177
    85
    val casedist_thms = map prove_casedist_thm ((0 upto (length newTs - 1)) ~~
berghofe@5177
    86
      (DatatypeProp.make_casedists descr sorts) ~~ newTs)
wenzelm@8436
    87
  in thy |> store_thms_atts "exhaust" new_type_names (map single case_names_exhausts) casedist_thms end;
berghofe@5177
    88
berghofe@5177
    89
berghofe@5177
    90
(*************************** primrec combinators ******************************)
berghofe@5177
    91
berghofe@5661
    92
fun prove_primrec_thms flat_names new_type_names descr sorts
berghofe@7015
    93
    (dt_info : datatype_info Symtab.table) constr_inject dist_rewrites dist_ss induct thy =
berghofe@5177
    94
  let
wenzelm@6427
    95
    val _ = message "Constructing primrec combinators ...";
berghofe@5661
    96
berghofe@5661
    97
    val big_name = space_implode "_" new_type_names;
berghofe@5661
    98
    val thy0 = add_path flat_names big_name thy;
berghofe@5177
    99
skalberg@15570
   100
    val descr' = List.concat descr;
berghofe@5177
   101
    val recTs = get_rec_types descr' sorts;
skalberg@15574
   102
    val used = foldr add_typ_tfree_names [] recTs;
skalberg@15570
   103
    val newTs = Library.take (length (hd descr), recTs);
berghofe@5177
   104
wenzelm@8305
   105
    val induct_Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct)));
berghofe@5177
   106
berghofe@5661
   107
    val big_rec_name' = big_name ^ "_rec_set";
wenzelm@6394
   108
    val rec_set_names = map (Sign.full_name (Theory.sign_of thy0))
berghofe@5177
   109
      (if length descr' = 1 then [big_rec_name'] else
berghofe@5177
   110
        (map ((curry (op ^) (big_rec_name' ^ "_")) o string_of_int)
berghofe@5177
   111
          (1 upto (length descr'))));
berghofe@5177
   112
berghofe@15459
   113
    val (rec_result_Ts, reccomb_fn_Ts) = DatatypeProp.make_primrec_Ts descr sorts used;
berghofe@5177
   114
berghofe@5177
   115
    val rec_set_Ts = map (fn (T1, T2) => reccomb_fn_Ts ---> HOLogic.mk_setT
berghofe@5177
   116
      (HOLogic.mk_prodT (T1, T2))) (recTs ~~ rec_result_Ts);
berghofe@5177
   117
berghofe@5177
   118
    val rec_fns = map (uncurry (mk_Free "f"))
berghofe@5177
   119
      (reccomb_fn_Ts ~~ (1 upto (length reccomb_fn_Ts)));
berghofe@5177
   120
    val rec_sets = map (fn c => list_comb (Const c, rec_fns))
berghofe@5177
   121
      (rec_set_names ~~ rec_set_Ts);
berghofe@5177
   122
berghofe@5177
   123
    (* introduction rules for graph of primrec function *)
berghofe@5177
   124
berghofe@5177
   125
    fun make_rec_intr T set_name ((rec_intr_ts, l), (cname, cargs)) =
berghofe@5177
   126
      let
berghofe@7015
   127
        fun mk_prem ((dt, U), (j, k, prems, t1s, t2s)) =
berghofe@7015
   128
          let val free1 = mk_Free "x" U j
berghofe@13641
   129
          in (case (strip_dtyp dt, strip_type U) of
berghofe@13641
   130
             ((_, DtRec m), (Us, _)) =>
berghofe@13641
   131
               let
skalberg@15570
   132
                 val free2 = mk_Free "y" (Us ---> List.nth (rec_result_Ts, m)) k;
berghofe@13641
   133
                 val i = length Us
berghofe@13641
   134
               in (j + 1, k + 1, HOLogic.mk_Trueprop (HOLogic.list_all
berghofe@13641
   135
                     (map (pair "x") Us, HOLogic.mk_mem (HOLogic.mk_prod
berghofe@13641
   136
                       (app_bnds free1 i, app_bnds free2 i),
skalberg@15570
   137
                         List.nth (rec_sets, m)))) :: prems,
berghofe@5177
   138
                   free1::t1s, free2::t2s)
berghofe@5177
   139
               end
berghofe@5177
   140
           | _ => (j + 1, k, prems, free1::t1s, t2s))
berghofe@5177
   141
          end;
berghofe@5177
   142
berghofe@5177
   143
        val Ts = map (typ_of_dtyp descr' sorts) cargs;
skalberg@15574
   144
        val (_, _, prems, t1s, t2s) = foldr mk_prem (1, 1, [], [], []) (cargs ~~ Ts)
berghofe@5177
   145
berghofe@5177
   146
      in (rec_intr_ts @ [Logic.list_implies (prems, HOLogic.mk_Trueprop (HOLogic.mk_mem
berghofe@5177
   147
        (HOLogic.mk_prod (list_comb (Const (cname, Ts ---> T), t1s),
skalberg@15570
   148
          list_comb (List.nth (rec_fns, l), t1s @ t2s)), set_name)))], l + 1)
berghofe@5177
   149
      end;
berghofe@5177
   150
skalberg@15570
   151
    val (rec_intr_ts, _) = Library.foldl (fn (x, ((d, T), set_name)) =>
skalberg@15570
   152
      Library.foldl (make_rec_intr T set_name) (x, #3 (snd d)))
berghofe@5177
   153
        (([], 0), descr' ~~ recTs ~~ rec_sets);
berghofe@5177
   154
berghofe@5177
   155
    val (thy1, {intrs = rec_intrs, elims = rec_elims, ...}) =
berghofe@5661
   156
      setmp InductivePackage.quiet_mode (!quiet_mode)
berghofe@5661
   157
        (InductivePackage.add_inductive_i false true big_rec_name' false false true
berghofe@13641
   158
           rec_sets (map (fn x => (("", x), [])) rec_intr_ts) []) thy0;
berghofe@5177
   159
berghofe@5177
   160
    (* prove uniqueness and termination of primrec combinators *)
berghofe@5177
   161
wenzelm@6427
   162
    val _ = message "Proving termination and uniqueness of primrec functions ...";
berghofe@5177
   163
berghofe@5177
   164
    fun mk_unique_tac ((tac, intrs), ((((i, (tname, _, constrs)), elim), T), T')) =
berghofe@5177
   165
      let
berghofe@5177
   166
        val distinct_tac = (etac Pair_inject 1) THEN
berghofe@5177
   167
          (if i < length newTs then
skalberg@15570
   168
             full_simp_tac (HOL_ss addsimps (List.nth (dist_rewrites, i))) 1
berghofe@7015
   169
           else full_simp_tac dist_ss 1);
berghofe@5177
   170
berghofe@5177
   171
        val inject = map (fn r => r RS iffD1)
skalberg@15570
   172
          (if i < length newTs then List.nth (constr_inject, i)
wenzelm@17412
   173
            else #inject (the (Symtab.lookup dt_info tname)));
berghofe@5177
   174
berghofe@5177
   175
        fun mk_unique_constr_tac n ((tac, intr::intrs, j), (cname, cargs)) =
berghofe@5177
   176
          let
skalberg@15570
   177
            val k = length (List.filter is_rec_type cargs)
berghofe@5177
   178
berghofe@5177
   179
          in (EVERY [DETERM tac,
berghofe@5177
   180
                REPEAT (etac ex1E 1), rtac ex1I 1,
berghofe@5177
   181
                DEPTH_SOLVE_1 (ares_tac [intr] 1),
berghofe@13641
   182
                REPEAT_DETERM_N k (etac thin_rl 1 THEN rotate_tac 1 1),
berghofe@5177
   183
                etac elim 1,
berghofe@5177
   184
                REPEAT_DETERM_N j distinct_tac,
berghofe@5177
   185
                etac Pair_inject 1, TRY (dresolve_tac inject 1),
berghofe@5177
   186
                REPEAT (etac conjE 1), hyp_subst_tac 1,
berghofe@13641
   187
                REPEAT (EVERY [etac allE 1, dtac mp 1, atac 1]),
berghofe@5177
   188
                TRY (hyp_subst_tac 1),
berghofe@5177
   189
                rtac refl 1,
berghofe@5177
   190
                REPEAT_DETERM_N (n - j - 1) distinct_tac],
berghofe@5177
   191
              intrs, j + 1)
berghofe@5177
   192
          end;
berghofe@5177
   193
skalberg@15570
   194
        val (tac', intrs', _) = Library.foldl (mk_unique_constr_tac (length constrs))
berghofe@5177
   195
          ((tac, intrs, 0), constrs);
berghofe@5177
   196
berghofe@5177
   197
      in (tac', intrs') end;
berghofe@5177
   198
berghofe@5177
   199
    val rec_unique_thms =
berghofe@5177
   200
      let
berghofe@5177
   201
        val rec_unique_ts = map (fn (((set_t, T1), T2), i) =>
berghofe@5177
   202
          Const ("Ex1", (T2 --> HOLogic.boolT) --> HOLogic.boolT) $
berghofe@5177
   203
            absfree ("y", T2, HOLogic.mk_mem (HOLogic.mk_prod
berghofe@5177
   204
              (mk_Free "x" T1 i, Free ("y", T2)), set_t)))
berghofe@5177
   205
                (rec_sets ~~ recTs ~~ rec_result_Ts ~~ (1 upto length recTs));
wenzelm@17985
   206
        val cert = cterm_of thy1
berghofe@5177
   207
        val insts = map (fn ((i, T), t) => absfree ("x" ^ (string_of_int i), T, t))
berghofe@5177
   208
          ((1 upto length recTs) ~~ recTs ~~ rec_unique_ts);
berghofe@5177
   209
        val induct' = cterm_instantiate ((map cert induct_Ps) ~~
berghofe@5177
   210
          (map cert insts)) induct;
skalberg@15570
   211
        val (tac, _) = Library.foldl mk_unique_tac
berghofe@13641
   212
          (((rtac induct' THEN_ALL_NEW ObjectLogic.atomize_tac) 1
berghofe@13641
   213
              THEN rewtac (mk_meta_eq choice_eq), rec_intrs),
wenzelm@10911
   214
            descr' ~~ rec_elims ~~ recTs ~~ rec_result_Ts);
berghofe@5177
   215
wenzelm@17985
   216
      in split_conj_thm (standard (Goal.prove thy1 [] []
wenzelm@17985
   217
        (HOLogic.mk_Trueprop (mk_conj rec_unique_ts)) (K tac)))
berghofe@5177
   218
      end;
berghofe@5177
   219
wenzelm@11435
   220
    val rec_total_thms = map (fn r => r RS theI') rec_unique_thms;
berghofe@5177
   221
berghofe@5177
   222
    (* define primrec combinators *)
berghofe@5177
   223
berghofe@5177
   224
    val big_reccomb_name = (space_implode "_" new_type_names) ^ "_rec";
wenzelm@6394
   225
    val reccomb_names = map (Sign.full_name (Theory.sign_of thy1))
berghofe@5177
   226
      (if length descr' = 1 then [big_reccomb_name] else
berghofe@5177
   227
        (map ((curry (op ^) (big_reccomb_name ^ "_")) o string_of_int)
berghofe@5177
   228
          (1 upto (length descr'))));
berghofe@5177
   229
    val reccombs = map (fn ((name, T), T') => list_comb
berghofe@5177
   230
      (Const (name, reccomb_fn_Ts @ [T] ---> T'), rec_fns))
berghofe@5177
   231
        (reccomb_names ~~ recTs ~~ rec_result_Ts);
berghofe@5177
   232
wenzelm@8436
   233
    val (thy2, reccomb_defs) = thy1 |>
berghofe@5177
   234
      Theory.add_consts_i (map (fn ((name, T), T') =>
berghofe@5177
   235
        (Sign.base_name name, reccomb_fn_Ts @ [T] ---> T', NoSyn))
berghofe@5177
   236
          (reccomb_names ~~ recTs ~~ rec_result_Ts)) |>
wenzelm@9315
   237
      (PureThy.add_defs_i false o map Thm.no_attributes) (map (fn ((((name, comb), set), T), T') =>
berghofe@7015
   238
        ((Sign.base_name name) ^ "_def", Logic.mk_equals (comb, absfree ("x", T,
wenzelm@11435
   239
           Const ("The", (T' --> HOLogic.boolT) --> T') $ absfree ("y", T',
berghofe@7015
   240
             HOLogic.mk_mem (HOLogic.mk_prod (Free ("x", T), Free ("y", T')), set))))))
wenzelm@8436
   241
               (reccomb_names ~~ reccombs ~~ rec_sets ~~ recTs ~~ rec_result_Ts)) |>>
berghofe@5661
   242
      parent_path flat_names;
berghofe@5177
   243
berghofe@5177
   244
berghofe@5177
   245
    (* prove characteristic equations for primrec combinators *)
berghofe@5177
   246
wenzelm@6427
   247
    val _ = message "Proving characteristic theorems for primrec combinators ..."
berghofe@5177
   248
wenzelm@17985
   249
    val rec_thms = map (fn t => standard (Goal.prove thy2 [] [] t
wenzelm@17985
   250
      (fn _ => EVERY
wenzelm@17985
   251
        [rewrite_goals_tac reccomb_defs,
wenzelm@17985
   252
         rtac the1_equality 1,
berghofe@5177
   253
         resolve_tac rec_unique_thms 1,
berghofe@5177
   254
         resolve_tac rec_intrs 1,
wenzelm@17985
   255
         REPEAT (rtac allI 1 ORELSE resolve_tac rec_total_thms 1)])))
berghofe@5177
   256
           (DatatypeProp.make_primrecs new_type_names descr sorts thy2)
berghofe@5177
   257
berghofe@5177
   258
  in
berghofe@8477
   259
    thy2 |> Theory.add_path (space_implode "_" new_type_names) |>
berghofe@8477
   260
    PureThy.add_thmss [(("recs", rec_thms), [])] |>>
skalberg@15570
   261
    Theory.parent_path |> apsnd (pair reccomb_names o List.concat)
berghofe@5177
   262
  end;
berghofe@5177
   263
berghofe@8477
   264
berghofe@5177
   265
(***************************** case combinators *******************************)
berghofe@5177
   266
berghofe@5661
   267
fun prove_case_thms flat_names new_type_names descr sorts reccomb_names primrec_thms thy =
berghofe@5177
   268
  let
wenzelm@6427
   269
    val _ = message "Proving characteristic theorems for case combinators ...";
berghofe@5661
   270
berghofe@5661
   271
    val thy1 = add_path flat_names (space_implode "_" new_type_names) thy;
berghofe@5177
   272
skalberg@15570
   273
    val descr' = List.concat descr;
berghofe@5177
   274
    val recTs = get_rec_types descr' sorts;
skalberg@15574
   275
    val used = foldr add_typ_tfree_names [] recTs;
skalberg@15570
   276
    val newTs = Library.take (length (hd descr), recTs);
wenzelm@12338
   277
    val T' = TFree (variant used "'t", HOLogic.typeS);
berghofe@5177
   278
berghofe@13641
   279
    fun mk_dummyT dt = binder_types (typ_of_dtyp descr' sorts dt) ---> T';
berghofe@7015
   280
berghofe@5177
   281
    val case_dummy_fns = map (fn (_, (_, _, constrs)) => map (fn (_, cargs) =>
berghofe@5177
   282
      let
berghofe@5177
   283
        val Ts = map (typ_of_dtyp descr' sorts) cargs;
skalberg@15570
   284
        val Ts' = map mk_dummyT (List.filter is_rec_type cargs)
berghofe@5578
   285
      in Const ("arbitrary", Ts @ Ts' ---> T')
berghofe@5177
   286
      end) constrs) descr';
berghofe@5177
   287
berghofe@5177
   288
    val case_names = map (fn s =>
wenzelm@6394
   289
      Sign.full_name (Theory.sign_of thy1) (s ^ "_case")) new_type_names;
berghofe@5177
   290
berghofe@5177
   291
    (* define case combinators via primrec combinators *)
berghofe@5177
   292
skalberg@15570
   293
    val (case_defs, thy2) = Library.foldl (fn ((defs, thy),
berghofe@5177
   294
      ((((i, (_, _, constrs)), T), name), recname)) =>
berghofe@5177
   295
        let
berghofe@5177
   296
          val (fns1, fns2) = ListPair.unzip (map (fn ((_, cargs), j) =>
berghofe@5177
   297
            let
berghofe@5177
   298
              val Ts = map (typ_of_dtyp descr' sorts) cargs;
skalberg@15570
   299
              val Ts' = Ts @ map mk_dummyT (List.filter is_rec_type cargs);
berghofe@5177
   300
              val frees' = map (uncurry (mk_Free "x")) (Ts' ~~ (1 upto length Ts'));
skalberg@15570
   301
              val frees = Library.take (length cargs, frees');
berghofe@5177
   302
              val free = mk_Free "f" (Ts ---> T') j
berghofe@5177
   303
            in
berghofe@5177
   304
             (free, list_abs_free (map dest_Free frees',
berghofe@5177
   305
               list_comb (free, frees)))
berghofe@5177
   306
            end) (constrs ~~ (1 upto length constrs)));
berghofe@5177
   307
berghofe@5177
   308
          val caseT = (map (snd o dest_Free) fns1) @ [T] ---> T';
skalberg@15570
   309
          val fns = (List.concat (Library.take (i, case_dummy_fns))) @
skalberg@15570
   310
            fns2 @ (List.concat (Library.drop (i + 1, case_dummy_fns)));
berghofe@5177
   311
          val reccomb = Const (recname, (map fastype_of fns) @ [T] ---> T');
berghofe@5177
   312
          val decl = (Sign.base_name name, caseT, NoSyn);
berghofe@5177
   313
          val def = ((Sign.base_name name) ^ "_def",
berghofe@5177
   314
            Logic.mk_equals (list_comb (Const (name, caseT), fns1),
skalberg@15570
   315
              list_comb (reccomb, (List.concat (Library.take (i, case_dummy_fns))) @
skalberg@15570
   316
                fns2 @ (List.concat (Library.drop (i + 1, case_dummy_fns))) )));
wenzelm@8436
   317
          val (thy', [def_thm]) = thy |>
wenzelm@9315
   318
            Theory.add_consts_i [decl] |> (PureThy.add_defs_i false o map Thm.no_attributes) [def];
berghofe@5177
   319
wenzelm@8436
   320
        in (defs @ [def_thm], thy')
berghofe@5661
   321
        end) (([], thy1), (hd descr) ~~ newTs ~~ case_names ~~
skalberg@15570
   322
          (Library.take (length newTs, reccomb_names)));
berghofe@5177
   323
wenzelm@17985
   324
    val case_thms = map (map (fn t => standard (Goal.prove thy2 [] [] t
wenzelm@17985
   325
      (fn _ => EVERY [rewrite_goals_tac (case_defs @ map mk_meta_eq primrec_thms), rtac refl 1]))))
berghofe@8477
   326
          (DatatypeProp.make_cases new_type_names descr sorts thy2)
berghofe@5177
   327
berghofe@8477
   328
  in
berghofe@14799
   329
    thy2 |>
berghofe@8477
   330
    parent_path flat_names |>
berghofe@8477
   331
    store_thmss "cases" new_type_names case_thms |>
berghofe@8477
   332
    apsnd (rpair case_names)
berghofe@8477
   333
  end;
berghofe@5177
   334
berghofe@5177
   335
berghofe@5177
   336
(******************************* case splitting *******************************)
berghofe@5177
   337
berghofe@5177
   338
fun prove_split_thms new_type_names descr sorts constr_inject dist_rewrites
berghofe@5177
   339
    casedist_thms case_thms thy =
berghofe@5177
   340
  let
wenzelm@6427
   341
    val _ = message "Proving equations for case splitting ...";
berghofe@5177
   342
skalberg@15570
   343
    val descr' = List.concat descr;
berghofe@5177
   344
    val recTs = get_rec_types descr' sorts;
skalberg@15570
   345
    val newTs = Library.take (length (hd descr), recTs);
berghofe@5177
   346
berghofe@5177
   347
    fun prove_split_thms ((((((t1, t2), inject), dist_rewrites'),
berghofe@5177
   348
        exhaustion), case_thms'), T) =
berghofe@5177
   349
      let
wenzelm@17985
   350
        val cert = cterm_of thy;
berghofe@5177
   351
        val _ $ (_ $ lhs $ _) = hd (Logic.strip_assums_hyp (hd (prems_of exhaustion)));
berghofe@5177
   352
        val exhaustion' = cterm_instantiate
berghofe@5177
   353
          [(cert lhs, cert (Free ("x", T)))] exhaustion;
wenzelm@17985
   354
        val tacf = K (EVERY [rtac exhaustion' 1, ALLGOALS (asm_simp_tac
wenzelm@17985
   355
          (HOL_ss addsimps (dist_rewrites' @ inject @ case_thms')))])
berghofe@5177
   356
      in
wenzelm@17985
   357
        (standard (Goal.prove thy [] [] t1 tacf),
wenzelm@17985
   358
         standard (Goal.prove thy [] [] t2 tacf))
berghofe@5177
   359
      end;
berghofe@5177
   360
berghofe@5177
   361
    val split_thm_pairs = map prove_split_thms
berghofe@5177
   362
      ((DatatypeProp.make_splits new_type_names descr sorts thy) ~~ constr_inject ~~
berghofe@5177
   363
        dist_rewrites ~~ casedist_thms ~~ case_thms ~~ newTs);
berghofe@5177
   364
berghofe@5177
   365
    val (split_thms, split_asm_thms) = ListPair.unzip split_thm_pairs
berghofe@5177
   366
berghofe@5177
   367
  in
wenzelm@8436
   368
    thy |> store_thms "split" new_type_names split_thms |>>>
wenzelm@8436
   369
      store_thms "split_asm" new_type_names split_asm_thms |> apsnd ListPair.zip
berghofe@5177
   370
  end;
berghofe@5177
   371
berghofe@5177
   372
(******************************* size functions *******************************)
berghofe@5177
   373
berghofe@5661
   374
fun prove_size_thms flat_names new_type_names descr sorts reccomb_names primrec_thms thy =
berghofe@13641
   375
  if exists (fn (_, (_, _, constrs)) => exists (fn (_, cargs) => exists (fn dt =>
berghofe@13641
   376
    is_rec_type dt andalso not (null (fst (strip_dtyp dt)))) cargs) constrs)
skalberg@15570
   377
      (List.concat descr)
berghofe@7015
   378
  then
berghofe@7015
   379
    (thy, [])
berghofe@7015
   380
  else
berghofe@5177
   381
  let
wenzelm@6427
   382
    val _ = message "Proving equations for size function ...";
berghofe@5661
   383
berghofe@5661
   384
    val big_name = space_implode "_" new_type_names;
berghofe@5661
   385
    val thy1 = add_path flat_names big_name thy;
berghofe@5177
   386
skalberg@15570
   387
    val descr' = List.concat descr;
berghofe@5177
   388
    val recTs = get_rec_types descr' sorts;
berghofe@5177
   389
wenzelm@11957
   390
    val size_name = "Nat.size";
berghofe@5177
   391
    val size_names = replicate (length (hd descr)) size_name @
berghofe@9739
   392
      map (Sign.full_name (Theory.sign_of thy1)) (DatatypeProp.indexify_names
skalberg@15570
   393
        (map (fn T => name_of_typ T ^ "_size") (Library.drop (length (hd descr), recTs))));
berghofe@9739
   394
    val def_names = map (fn s => s ^ "_def") (DatatypeProp.indexify_names
berghofe@9739
   395
      (map (fn T => name_of_typ T ^ "_size") recTs));
berghofe@5177
   396
wenzelm@7704
   397
    fun plus (t1, t2) = Const ("op +", [HOLogic.natT, HOLogic.natT] ---> HOLogic.natT) $ t1 $ t2;
berghofe@5177
   398
berghofe@5177
   399
    fun make_sizefun (_, cargs) =
berghofe@5177
   400
      let
berghofe@5177
   401
        val Ts = map (typ_of_dtyp descr' sorts) cargs;
skalberg@15570
   402
        val k = length (List.filter is_rec_type cargs);
berghofe@5177
   403
        val t = if k = 0 then HOLogic.zero else
wenzelm@7704
   404
          foldl1 plus (map Bound (k - 1 downto 0) @ [HOLogic.mk_nat 1])
berghofe@5177
   405
      in
skalberg@15574
   406
        foldr (fn (T, t') => Abs ("x", T, t')) t (Ts @ replicate k HOLogic.natT)
berghofe@5177
   407
      end;
berghofe@5177
   408
skalberg@15570
   409
    val fs = List.concat (map (fn (_, (_, _, constrs)) => map make_sizefun constrs) descr');
berghofe@5177
   410
    val fTs = map fastype_of fs;
berghofe@5177
   411
wenzelm@8436
   412
    val (thy', size_def_thms) = thy1 |>
berghofe@5177
   413
      Theory.add_consts_i (map (fn (s, T) =>
berghofe@5177
   414
        (Sign.base_name s, T --> HOLogic.natT, NoSyn))
skalberg@15570
   415
          (Library.drop (length (hd descr), size_names ~~ recTs))) |>
wenzelm@9315
   416
      (PureThy.add_defs_i true o map Thm.no_attributes) (map (fn (((s, T), def_name), rec_name) =>
berghofe@5177
   417
        (def_name, Logic.mk_equals (Const (s, T --> HOLogic.natT),
berghofe@5177
   418
          list_comb (Const (rec_name, fTs @ [T] ---> HOLogic.natT), fs))))
wenzelm@8436
   419
            (size_names ~~ recTs ~~ def_names ~~ reccomb_names)) |>>
berghofe@5661
   420
      parent_path flat_names;
berghofe@5177
   421
oheimb@5553
   422
    val rewrites = size_def_thms @ map mk_meta_eq primrec_thms;
berghofe@5177
   423
wenzelm@17985
   424
    val size_thms = map (fn t => standard (Goal.prove thy' [] [] t
wenzelm@17985
   425
      (fn _ => EVERY [rewrite_goals_tac rewrites, rtac refl 1])))
berghofe@9739
   426
        (DatatypeProp.make_size descr sorts thy')
berghofe@5177
   427
berghofe@5177
   428
  in
berghofe@8477
   429
    thy' |> Theory.add_path big_name |>
berghofe@8477
   430
    PureThy.add_thmss [(("size", size_thms), [])] |>>
skalberg@15570
   431
    Theory.parent_path |> apsnd List.concat
berghofe@5177
   432
  end;
berghofe@5177
   433
nipkow@8601
   434
fun prove_weak_case_congs new_type_names descr sorts thy =
nipkow@8601
   435
  let
nipkow@8601
   436
    fun prove_weak_case_cong t =
wenzelm@17985
   437
       standard (Goal.prove thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t)
wenzelm@17985
   438
         (fn prems => EVERY [rtac ((hd prems) RS arg_cong) 1]))
nipkow@8601
   439
nipkow@8601
   440
    val weak_case_congs = map prove_weak_case_cong (DatatypeProp.make_weak_case_congs
nipkow@8601
   441
      new_type_names descr sorts thy)
nipkow@8601
   442
nipkow@8601
   443
  in thy |> store_thms "weak_case_cong" new_type_names weak_case_congs end;
berghofe@8477
   444
berghofe@5177
   445
(************************* additional theorems for TFL ************************)
berghofe@5177
   446
berghofe@5177
   447
fun prove_nchotomys new_type_names descr sorts casedist_thms thy =
berghofe@5177
   448
  let
wenzelm@6427
   449
    val _ = message "Proving additional theorems for TFL ...";
berghofe@5177
   450
berghofe@5177
   451
    fun prove_nchotomy (t, exhaustion) =
berghofe@5177
   452
      let
berghofe@5177
   453
        (* For goal i, select the correct disjunct to attack, then prove it *)
berghofe@5177
   454
        fun tac i 0 = EVERY [TRY (rtac disjI1 i),
berghofe@5177
   455
              hyp_subst_tac i, REPEAT (rtac exI i), rtac refl i]
berghofe@5177
   456
          | tac i n = rtac disjI2 i THEN tac i (n - 1)
berghofe@5177
   457
      in 
wenzelm@17985
   458
        standard (Goal.prove thy [] [] t (fn _ =>
wenzelm@17985
   459
          EVERY [rtac allI 1,
berghofe@5177
   460
           exh_tac (K exhaustion) 1,
wenzelm@17985
   461
           ALLGOALS (fn i => tac i (i-1))]))
berghofe@5177
   462
      end;
berghofe@5177
   463
berghofe@5177
   464
    val nchotomys =
berghofe@5177
   465
      map prove_nchotomy (DatatypeProp.make_nchotomys descr sorts ~~ casedist_thms)
berghofe@5177
   466
wenzelm@8436
   467
  in thy |> store_thms "nchotomy" new_type_names nchotomys end;
berghofe@5177
   468
berghofe@5177
   469
fun prove_case_congs new_type_names descr sorts nchotomys case_thms thy =
berghofe@5177
   470
  let
berghofe@5177
   471
    fun prove_case_cong ((t, nchotomy), case_rewrites) =
berghofe@5177
   472
      let
berghofe@5177
   473
        val (Const ("==>", _) $ tm $ _) = t;
berghofe@5177
   474
        val (Const ("Trueprop", _) $ (Const ("op =", _) $ _ $ Ma)) = tm;
wenzelm@6394
   475
        val cert = cterm_of (Theory.sign_of thy);
berghofe@5177
   476
        val nchotomy' = nchotomy RS spec;
berghofe@5177
   477
        val nchotomy'' = cterm_instantiate
berghofe@5177
   478
          [(cert (hd (add_term_vars (concl_of nchotomy', []))), cert Ma)] nchotomy'
berghofe@5177
   479
      in
wenzelm@17985
   480
        standard (Goal.prove thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t)
wenzelm@17985
   481
          (fn prems => 
wenzelm@17985
   482
            let val simplify = asm_simp_tac (HOL_ss addsimps (prems @ case_rewrites))
wenzelm@17985
   483
            in EVERY [simp_tac (HOL_ss addsimps [hd prems]) 1,
wenzelm@17985
   484
                cut_facts_tac [nchotomy''] 1,
wenzelm@17985
   485
                REPEAT (etac disjE 1 THEN REPEAT (etac exE 1) THEN simplify 1),
wenzelm@17985
   486
                REPEAT (etac exE 1) THEN simplify 1 (* Get last disjunct *)]
wenzelm@17985
   487
            end))
berghofe@5177
   488
      end;
berghofe@5177
   489
berghofe@5177
   490
    val case_congs = map prove_case_cong (DatatypeProp.make_case_congs
berghofe@5177
   491
      new_type_names descr sorts thy ~~ nchotomys ~~ case_thms)
berghofe@5177
   492
wenzelm@8436
   493
  in thy |> store_thms "case_cong" new_type_names case_congs end;
berghofe@5177
   494
berghofe@5177
   495
end;